How to get Mirrored-Repeat texture extension / UV in 2.8
At its simplest, with a UV map like this:

.. which I think is equivalent to yours?
Then all you have to do is put a Math &gt; Ping-Pong node in the way of the X and Y outputs of the UV texture space, on the way into the image:

If you find you need to tweak offsets, scales of the repeat, you may find it easier to wrap Ping-Pong up with something like the 'Triangle Wave' group you can download from this answer.
If you have several different UV maps, then instead of the Texture Coordinate input node, you would use a UV Map input node, to select the right one.